## Simplifying Expressions

In algebra, letters are used to stand for numbers.

The letters are often called variables.

It is necessary to be able to add, subtract, multipy and divide algebraic terms.

The BEDMAS rule applies to algebra, as well as numbers.

### Definitions

• An algebraic term is made up of a coefficient, variables and exponents.
• e.g. -4x2y
• -4 is the coefficient

x and y are the variables

2 is an exponent of the variable x

• Like terms have the same variables and exponents.
• e.g. { 2a, 4a, -6a } are like terms. a is common to all.
• { 4a2, a, 6 } are unlike terms. There is no common term.

{ab, 2ab, -4ab } are like terms. ab is common to all.

{a2b, ab 2, 3ab } are unlike terms. There is no common term.

• An algebraic expression is a group of terms.
• e.g. 4x + 3y and 4x2y − 3xy are expressions.

An expression involving addition and subtraction can be simplified only if it contains like terms.

The like terms are collected together and then added or subtracted.

 Examples Answers Simplify: (a) 4a + 6a (a) 4a + 6a = 10a (b) 12pq − 6pq + 4pq (b) 12pq − 6pq + 4pq = 10pq (c) 3c + 4d + 5c (c) 3c + 4d + 5c = 3c + 5c + 4d = 8c + 4d (d) 2x2 + x + 5x2 − 3x (d) 2x2 + x + 5x2 − 3x= 2x2 + 5x2 + x − 3x= 7x2 − 2x

### Multiplication and Division

An expression involving multiplication and division can be simplified using the laws of indices. (see Topic 8)
Note that a dot is used to signify multiplication.

 Examples Answers Simplify: (a) 3x . 2x (a) 3x . 2x = 6x2 (b) 4p . -2q (b) 4p . -2q = -8pq (c) (c) 